Valve Stroking for Complex Piping Systems

A theory is developed for movement of valves in complex piping systems so that the transient ceases when the valve movement ceases. One pipe in the system is selected and the head-time relations determined so that this flow is adjusted in a controlled manner not exceeding predetermined head limits. In a complex system, the flow changes are apportioned among the branches as a linear relation of initial to final steady-state flow in each pipe. The combination of these two procedures leads to values of head and flow at each control point in the system; hence, the valves or other moving boundaries may be adjusted to cause the desired transient change to occur. Frictional effects are included in the analysis which is based on the method of characteristics solution of the transient flow equations. The theory has been verified experimentally and results are given for two cases using 4,000 ft of 0.95-in. copper tubing.